Constructing 3D motions from curvature and torsion profiles

A means for constructing a free-form motion in three dimensions is given. A sparse sequence of prescribed poses is used to guide the motion, and some of these can also be specified to be precision poses through which the motion must pass. The resultant motion is given in a sequence of refined poses. Geometric algebra is used to specify these in a way that is analogous to the use of complex numbers in an equivalent approach for free-form curves.

► Creation of three dimensional motions based on a given sparse sequence of poses.
► Extension of a method for creating a curve (in two dimensions) from a sparse sequence of points, by working in the complex plane.
► Use of geometric algebra (an extension of the quaternions) to enable the corresponding approach in three dimensions.